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A Latent Hidden Markov Model for Process Data

Published online by Cambridge University Press:  01 January 2025

Xueying Tang Open the ORCID record for Xueying Tang [Opens in a new window]
Xueying Tang*
Affiliation:
University of Arizona
*
Correspondence should be made to Xueying Tang, University of Arizona, 617 N. Santa Rita Ave., Tucson, AZ 85721, USA. Email: [email protected]
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Abstract

Response process data from computer-based problem-solving items describe respondents’ problem-solving processes as sequences of actions. Such data provide a valuable source for understanding respondents’ problem-solving behaviors. Recently, data-driven feature extraction methods have been developed to compress the information in unstructured process data into relatively low-dimensional features. Although the extracted features can be used as covariates in regression or other models to understand respondents’ response behaviors, the results are often not easy to interpret since the relationship between the extracted features, and the original response process is often not explicitly defined. In this paper, we propose a statistical model for describing response processes and how they vary across respondents. The proposed model assumes a response process follows a hidden Markov model given the respondent’s latent traits. The structure of hidden Markov models resembles problem-solving processes, with the hidden states interpreted as problem-solving subtasks or stages. Incorporating the latent traits in hidden Markov models enables us to characterize the heterogeneity of response processes across respondents in a parsimonious and interpretable way. We demonstrate the performance of the proposed model through simulation experiments and case studies of PISA process data.

Keywords

response processlatent variablehidden Markov modelsproblem-solving behaviors
Type
Theory and Methods
Information
Psychometrika , Volume 89 , Issue 1 , March 2024 , pp. 205 - 240
Copyright
Copyright © 2023 The Author(s), under exclusive licence to The Psychometric Society.

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